What is the use of introducing the concepts of $\epsilon$-net in compactness.We know that if a set $A$ is totally bounded then for each $\epsilon>0$ ,there exists a finite $\epsilon$-nets in $A$.So,what is the use of defining it separately?Is it helpful in some other aspect?
2026-03-25 17:39:21.1774460361
What is the necessity of $\epsilon$-net?
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It works out that a metric space $X$ is compact iff it’s complete and totally bounded, so it’s important.